6 Questions
What is the property of an equation that states that if a = b, then b = a?
Symmetric Property
Which of the following equations is a quadratic equation?
x^2 + 4x + 4 = 0
What is the purpose of the Inverse Operations method in solving equations?
To use opposite operations to isolate the variable(s)
What is the result of applying the Addition/Subtraction Property to both sides of the equation 2x + 3 = 5?
2x = 5 - 3
Which of the following is an example of a linear equation?
2x + 3y = 7
What is the result of applying the Multiplication/Division Property to both sides of the equation 2x = 6?
x = 6/2
Study Notes
Equations
Definition
- An equation is a statement that says two mathematical expressions are equal.
- It is denoted by the equality symbol (=).
Types of Equations
-
Simple Equations: Equations in which the highest power of the variable(s) is 1.
- Example: 2x + 3 = 5
-
Quadratic Equations: Equations in which the highest power of the variable(s) is 2.
- Example: x^2 + 4x + 4 = 0
-
Linear Equations: Equations in which the highest power of the variable(s) is 1, and can be written in the form ax + by = c.
- Example: 2x + 3y = 7
Properties of Equations
- Reflexive Property: a = a (an equation is equal to itself)
- Symmetric Property: if a = b, then b = a (equations can be swapped)
- Transitive Property: if a = b and b = c, then a = c (equations can be chained)
Solving Equations
- Addition/Subtraction Property: adding or subtracting the same value to both sides of an equation does not change its solution.
- Multiplication/Division Property: multiplying or dividing both sides of an equation by a non-zero value does not change its solution.
-
Inverse Operations: using opposite operations to isolate the variable(s).
- Example: 2x = 6 → x = 6/2 → x = 3
Equations
Definition
- An equation is a statement that says two mathematical expressions are equal, denoted by the equality symbol (=).
Types of Equations
Simple Equations
- Equations in which the highest power of the variable(s) is 1.
- Example: 2x + 3 = 5
Quadratic Equations
- Equations in which the highest power of the variable(s) is 2.
- Example: x^2 + 4x + 4 = 0
Linear Equations
- Equations in which the highest power of the variable(s) is 1, and can be written in the form ax + by = c.
- Example: 2x + 3y = 7
Properties of Equations
Reflexive Property
- An equation is equal to itself (a = a).
Symmetric Property
- If a = b, then b = a (equations can be swapped).
Transitive Property
- If a = b and b = c, then a = c (equations can be chained).
Solving Equations
Addition/Subtraction Property
- Adding or subtracting the same value to both sides of an equation does not change its solution.
Multiplication/Division Property
- Multiplying or dividing both sides of an equation by a non-zero value does not change its solution.
Inverse Operations
- Using opposite operations to isolate the variable(s).
- Example: 2x = 6 → x = 6/2 → x = 3
Learn about the definition and types of equations, including simple, quadratic, and linear equations. Understand the concept of equality and powers of variables.
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